Nuprl Lemma : A-coerce_wf
∀[Val:Type]. ∀[n:ℕ]. ∀[AType:array{i:l}(Val;n)].
(A-coerce(array-model(AType)) ∈ ⋂T:Type. ((A-map'(array-model(AType)) T) ⟶ (A-map T)))
Proof
Definitions occuring in Statement :
A-coerce: A-coerce(AModel),
A-map': A-map'(AModel),
A-map: A-map,
array-model: array-model(AType),
array: array{i:l}(Val;n),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
apply: f a,
isect: ⋂x:A. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
array-model: array-model(AType),
A-coerce: A-coerce(AModel),
A-map: A-map,
A-map': A-map'(AModel),
pi2: snd(t),
pi1: fst(t),
array-monad: array-monad(AType),
M-map: M-map(mnd),
array-monad': array-monad'(AType),
mk_monad: mk_monad(M;return;bind)
Lemmas referenced :
array_wf,
nat_wf,
Arr_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
isect_memberEquality,
because_Cache,
universeEquality,
lambdaEquality,
independent_pairEquality,
applyEquality,
functionEquality
Latex:
\mforall{}[Val:Type]. \mforall{}[n:\mBbbN{}]. \mforall{}[AType:array\{i:l\}(Val;n)].
(A-coerce(array-model(AType)) \mmember{} \mcap{}T:Type. ((A-map'(array-model(AType)) T) {}\mrightarrow{} (A-map T)))
Date html generated:
2016_05_15-PM-02_18_52
Last ObjectModification:
2015_12_27-AM-08_58_37
Theory : monads
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